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<p><dfn class="terminology">Theorem</dfn> If <span class="process-math">\(p(x)\)</span> and <span class="process-math">\(q(x)\)</span> are continuous in the interval <span class="process-math">\(\alpha \le x \le \beta\)</span> which contains <span class="process-math">\(x_0\text{.}\)</span> Then the initial value problem (<a href="" class="xref" data-knowl="./knowl/eq2_10.html" title="Equation 2.1.10">(2.1.10)</a>) has a unique solution which is valid in the interval <span class="process-math">\((\alpha, \beta)\text{.}\)</span> (Theorem 2.4.1)</p>
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